Polytope of Type {2,4,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,10}*640
if this polytope has a name.
Group : SmallGroup(640,19898)
Rank : 5
Schlafli Type : {2,4,4,10}
Number of vertices, edges, etc : 2, 4, 8, 20, 10
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,4,10,2} of size 1280
Vertex Figure Of :
   {2,2,4,4,10} of size 1280
   {3,2,4,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,4,10}*320, {2,4,2,10}*320
   4-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
   5-fold quotients : {2,4,4,2}*128
   8-fold quotients : {2,2,2,5}*80
   10-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   20-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,4,10}*1280, {2,4,4,20}*1280, {2,4,8,10}*1280a, {2,8,4,10}*1280a, {2,4,8,10}*1280b, {2,8,4,10}*1280b, {2,4,4,10}*1280
   3-fold covers : {2,4,4,30}*1920, {6,4,4,10}*1920, {2,4,12,10}*1920a, {2,12,4,10}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (23,28)(24,29)(25,30)(26,31)(27,32)(33,38)(34,39)(35,40)(36,41)(37,42)
(63,68)(64,69)(65,70)(66,71)(67,72)(73,78)(74,79)(75,80)(76,81)(77,82);;
s2 := ( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)
(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(43,63)
(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)
(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(61,81)(62,82);;
s3 := ( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)
(13,53)(14,57)(15,56)(16,55)(17,54)(18,58)(19,62)(20,61)(21,60)(22,59)(23,73)
(24,77)(25,76)(26,75)(27,74)(28,78)(29,82)(30,81)(31,80)(32,79)(33,63)(34,67)
(35,66)(36,65)(37,64)(38,68)(39,72)(40,71)(41,70)(42,69);;
s4 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)
(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)
(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)
(80,82);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(82)!(1,2);
s1 := Sym(82)!(23,28)(24,29)(25,30)(26,31)(27,32)(33,38)(34,39)(35,40)(36,41)
(37,42)(63,68)(64,69)(65,70)(66,71)(67,72)(73,78)(74,79)(75,80)(76,81)(77,82);
s2 := Sym(82)!( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)
(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)
(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)
(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(61,81)(62,82);
s3 := Sym(82)!( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)
(12,49)(13,53)(14,57)(15,56)(16,55)(17,54)(18,58)(19,62)(20,61)(21,60)(22,59)
(23,73)(24,77)(25,76)(26,75)(27,74)(28,78)(29,82)(30,81)(31,80)(32,79)(33,63)
(34,67)(35,66)(36,65)(37,64)(38,68)(39,72)(40,71)(41,70)(42,69);
s4 := Sym(82)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)
(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)
(53,54)(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)
(80,82);
poly := sub<Sym(82)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope